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AstrometryWilliam F. van Altena ARAA (1983)
7. Conclusion
The field of astrometry is in the midst of a major revolution in terms of the accuracy obtained or expected in the near future for positions, proper motions, and parallaxes.
…
The Space Telescope should yield parallaxes better than 0.5 mas, and HIPPARCOS will produce around 100,000 parallaxes of the brighter stars good to around 2 mas.
…
Finally, radio astrometry offers the potential for obtaining precise positions, motions, and parallaxes for radio sources on an absolute system.
Radio Astrometry from the Milky Way to Distant Galaxies
Mark J. ReidHarvard-Smithsonian CfA
• Galactic Center Astrometry
• SFR Parallaxes & Proper Motions
• Extra-Galactic Proper Motions
• Ho from H2O Masers
Micro-arcsec Astrometry with the VLBA
Fringe spacing:
f~/D ~ 1 cm / 8000 km = 250 as
Centroid Precision:
0.5 f / SNR ~ 10 as
Systematics:
path length errors ~ 2 cm (~2 )
shift position by ~ 2f ~ 500 as
Relative positions (to QSOs):
~ 1 deg (0.02 rad)
cancel systematics: f ~ 10 asComparable to
GAIA & SIM
Galactic Center Stellar Orbits
• M = 4 x 106 Msun
• R < 50 AU
• Den. > 1017 Msun/pc3
Ghez et al / Genzel et al
What can radio observations tell us?...
VLT: 2 m
5”
0.04”
Where is the Galactic Center?
Combined IR + Radio astrometry shows Sgr A* at focal position of stellar orbits (+/-10 mas)
All stars there move fast. How fast does Sgr A* move?
• Parallel to Galactic Plane:
6.379 (+/- 0.024) mas/yr o/Ro = 29.5 km/s / kpc
• Perpendicular to Gal. Plane:
7.2 km/s motion of Sun
• Could re-define Galactic Plane
Now: HI & Sun in plane
New: LSR orbit & Sgr A* in plane
• Sgr A*’s motion to Gal. Plane
-0.4 +/- 0.9 km/s !
Proper Motion of Sgr A*
Reid & Brunthaler (2004)
IAU Gal. Plane
fit to data
Latest Results: Sgr A* Proper Motion
IR Stellar Orbits: MIR ~ 4 x 106 Msun
R < 50 AU
Radio Observations: Sgr A* motionless M > 10% of MIR
Observed size: R < 0.5 AU
IR + Radio data combined: • Dark mass = luminous source• Density > 1022 Msun/pc3
Overwhelming evidence for a Super-Massive Black Hole
Must Sgr A* be a SMBH?
Object Density Method Mass within Radius
(Msun/pc3) (Msun)
M 87 106 HST 3x109 7 pc
NGC 4258 1010 VLBA : H2O 4x107 0.1 pc
Sgr A* 1017 IR Star orbits 4x106 50 AU
Sgr A* >1022 VLBA p.m. >4x105 0.5 AU
SMBH 1024 3RSch 4x106 3*0.08 AU
3RSch = 30 as @ 8 kpc
VLBI (JCMT/SMA-ALMA-LMT-SMT-CARMA) @ 0.8 mm 20 asFringes: HawaiiArizona @ 1.3mm (60 as) ! (Doeleman et al 2008 Nature 455 78)
Orion Nebular Cluster Parallax
389 +/- 22 pc Sandstrom et al (2007)
437 +/- 19 pc Hirota et al (2007)
414 +/- 7 pc Menten et al (2007)
D = 414 +/- 7 pc
Menten, Reid, Forbrich & Brunthaler (2007)
W3OH Parallax
Schematic Model of Milky Way: Taylor-Cordes / Georgelin & Georgelin
• Dphoto ~ Dparallax
• Dk way off
• In Perseus Arm, not in Outer Arm
• Large peculiar V
Methanol Maser Parallaxes
Kinematic distances (Dk):
Problem: Dk > D
Partial fix: Ro < 8.5 kpc and/or o > 220 km/s Sgr A* p.m. requires o/Ro = 29.5 km/s/kpc = 236 / 8.0 = 251 / 8.5Brunthaler, Menten, Moscadelli, Reid, Xu, & Zheng
Honma et al; Hachisuka et al
Peculiar Motions of Star Forming Regions
• In rotating frame: Ro = 8.5 kpc o = 220 km/s
Clear systematic motions
• Update Galaxy model: Ro = 8.5 kpc o = 251 km/s
Systematic motions smaller, but significant
Peculiar Motions of Star Forming Regions
Galactic model: Ro = 8.5 kpc o = 251 km/s
& Solar Motion: U = 8 km/s V = 18 km/s W = 10 km/s
Residual motions considerably smaller
Solar Motion
Dehnen & Binney (1998) Hipparcos data in black
V Gal. Rot.
“Asymmetric Drift:” V appears larger when measured against older stars with higher dispersion
Late B-type
Maser p.m.
Massive stars born rotating ~13 km/s slower than Galaxy spins;
as they age, first speed up and then slow down again.
Asymmetric Drift
Massive Star Birth
Possible Sequence:
1. Molecular cloud in circular orbit
2. Hit by Spiral shock
3. Goes into elliptical orbit (near apocenter)
4. Compression triggers star formation
Extreme Supergiants
Extreme red supergiants with L 106 Lsun
“Fabulous 4”: NML Cyg, S Per, VY CMa, VX Sgr
H2O and SiO masers in circumstellar envelopes
VY CMa
0.4 < D < 1.8 kpc
Association with NGC 2362 D = 1.5 kpc (M-S fitting)
Parallax measured to be 1.1 kpc...
L = 3 x 105 Lsun (quite reasonable)
NGC 2362 cluster closer than thought?
Local Group Proper Motions
• 1920s van Maanen claimed to see M33 spin!
• mas/yr motions Spiral nebulae nearby (Galactic)
• Hubble argued more distant (extra-galactic)
• van Maanen’s error not found
M33
Extragalactic Proper Motions
• Parallax accuracy:
D ~ 10% at 10 kpc
can’t do galaxies yet
• Proper motion:
same techniques, but
~ T-3/2
• M33 & IC10
1) see spin (van Maanen)
2) see galaxy’s motion
M33
Andreas Brunthaler’s PhD Thesis
Extragalactic Proper Motions• M33/IC133 – M33/19 masers
VLBA: x = 30 +/- 2, y = 10 +/- 5 as/yr
HI: vx = 106 +/-20, vy = 35 +/- 20 km/s
D = 750 +/- 50 +/- 140 kpc
• Improvements in Rotation Model & 3rd maser source:
D < 10% possible
Brunthaler, Reid & Falcke
v
Tidal Heating of M33
• Try M31 proper motions; then calculate orbits
• Tidal heating of M33 for trial proper motions of M31:
M31 = (100,-100) km/s
( -50, -50) km/s
( 0, 0) km/s
~ 0 km/s M33 destroyed
~100 km/s M33 OK Loeb, Reid, Brunthaler & Falcke (2005)
NGC 4258 • Seyfert galaxy
• H2O masers in an edge-on, sub-parsec disk
• Rotation speed ~1000 km/s
• M ~ 3 x 107 Msun
• Geometric model D = 7.2 +/- 0.5 Mpc
• Used by Hubble Key Project to re-calibrate Cepheid PL relation
Herrnstein, Moran, Greenhill et al (1999)
AGN Maser Distance Measurements
A = V2 / R
R = D
D = V2 / A
R = D
V
High Velocity Maser Map
Drift of systemic masers over time
Systemic velocity masers
Red high-velocity masers
Blue high-velocity masers
• Goal: Ho accurate to 3%; constain Dark Energy Eq. of State
• How: Geometric Distances to H2O masers in Hubble Flow
GBT finds masers VLBA maps them
Maser Cosmology ProjectBraatz, Condon, Greenhill, Henkel, Lo & Reid
UGC 3789 map
• Similar to NGC 4258
Edge-on disk
Systemic vel. masers between red and blue high vel. masers
~7 times smaller angle
~7 times more distant
UGC 3789 Position-Velocity Diagram
• Keplerian high vel. masers
~107 Msun SMBH
• Systemic maser P-V ~ linear
(slight “bend” changing R)
• V = 625 km/s, = 0.52 mas
V
UGC 3789• Accelerations ~ 3.4 km/s/year
• D = V2 / A …Preliminary Analysis
V ~ 625 km/s
~ 0.52 mas
A ~ 3.4 km/s/yr
• Ho = Vcmb/D = 3385 km/s / 47 Mpc
= 72 +/- 7 +/- 4
from D Vcmb~200 km/s
• Comparable to Hubble Key Project!
D = 47 Mpc +/- 5
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